In multi-user radar applications, waveforms that show low cross-correlation and cross-ambiguity sidelobes are needed. In this study, the authors propose to generate novel multi-user waveforms using a modified version of Costas signals, namely doubly coded Costas signals. The modification principle consists in combining two Costas codes by coding the sub-pulses of the main code by another code. First, the sub-pulse Costas code diversity is used to generate waveforms with low cross-correlation sidelobes and good auto-correlation properties while using the same main Costas code. Conditions on sub-pulse codes are drawn by optimising the auto- and cross-ambiguity functions around the mainlobe. Subsequently, the authors extended the approach to the use of several main Costas codes selected according to particular criteria. Hence, since both main and sub-pulse Costas codes are exploited, the total number of generated signals is increased significantly compared with a usage of standard Costas codes. This can be suitable for multi-user radar applications with a large number of simultaneous users.